Question
Multiply polynomial $ \, \color{blue}{ x^2+4x-7 } \, $ by $ \, \color{orangered}{ x-3 }$.
Answer
$$ \left( \color{blue}{x^2+4x-7} \right) \cdot \left( \color{orangered}{x-3} \right) = x^3+x^2-19x+21 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{4x} & \color{blue}{-7} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{4x} & \color{blue}{-7} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{4x^2} & \color{orangered}{-7x} \\ \hline \color{blue}{-3} & \color{orangered}{-3x^2} & \color{orangered}{-12x} & \color{orangered}{21} \\ \hline \end{darray} $$Combine like terms:
$$ x^3 + 4x^2-3x^2-7x-12x + 21 = \\ x^3+x^2-19x+21 $$This page was created using
Polynomial Operations Calculator